3.101.96 \(\int \frac {8000+4800 x+960 x^2-56 x^3-12 x^4+(6000+2400 x+240 x^2-35 x^3) \log (x)+(1500+300 x) \log ^2(x)+125 \log ^3(x)}{(8000 x+4800 x^2+960 x^3+44 x^4-4 x^5+(6000 x+2400 x^2+240 x^3-5 x^4) \log (x)+(1500 x+300 x^2) \log ^2(x)+125 x \log ^3(x)) \log (\frac {160000 x+128000 x^2+38400 x^3+4320 x^4-64 x^5-32 x^6+x^7+(160000 x+96000 x^2+19200 x^3+880 x^4-80 x^5) \log (x)+(60000 x+24000 x^2+2400 x^3-50 x^4) \log ^2(x)+(10000 x+2000 x^2) \log ^3(x)+625 x \log ^4(x)}{160000+128000 x+38400 x^2+5120 x^3+256 x^4+(160000+96000 x+19200 x^2+1280 x^3) \log (x)+(60000+24000 x+2400 x^2) \log ^2(x)+(10000+2000 x) \log ^3(x)+625 \log ^4(x)})} \, dx\)

Optimal. Leaf size=28 \[ \log \left (\log \left (\frac {\left (x-\frac {x^4}{(-x+5 (4+x+\log (x)))^2}\right )^2}{x}\right )\right ) \]

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Rubi [F]  time = 9.28, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {8000+4800 x+960 x^2-56 x^3-12 x^4+\left (6000+2400 x+240 x^2-35 x^3\right ) \log (x)+(1500+300 x) \log ^2(x)+125 \log ^3(x)}{\left (8000 x+4800 x^2+960 x^3+44 x^4-4 x^5+\left (6000 x+2400 x^2+240 x^3-5 x^4\right ) \log (x)+\left (1500 x+300 x^2\right ) \log ^2(x)+125 x \log ^3(x)\right ) \log \left (\frac {160000 x+128000 x^2+38400 x^3+4320 x^4-64 x^5-32 x^6+x^7+\left (160000 x+96000 x^2+19200 x^3+880 x^4-80 x^5\right ) \log (x)+\left (60000 x+24000 x^2+2400 x^3-50 x^4\right ) \log ^2(x)+\left (10000 x+2000 x^2\right ) \log ^3(x)+625 x \log ^4(x)}{160000+128000 x+38400 x^2+5120 x^3+256 x^4+\left (160000+96000 x+19200 x^2+1280 x^3\right ) \log (x)+\left (60000+24000 x+2400 x^2\right ) \log ^2(x)+(10000+2000 x) \log ^3(x)+625 \log ^4(x)}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(8000 + 4800*x + 960*x^2 - 56*x^3 - 12*x^4 + (6000 + 2400*x + 240*x^2 - 35*x^3)*Log[x] + (1500 + 300*x)*Lo
g[x]^2 + 125*Log[x]^3)/((8000*x + 4800*x^2 + 960*x^3 + 44*x^4 - 4*x^5 + (6000*x + 2400*x^2 + 240*x^3 - 5*x^4)*
Log[x] + (1500*x + 300*x^2)*Log[x]^2 + 125*x*Log[x]^3)*Log[(160000*x + 128000*x^2 + 38400*x^3 + 4320*x^4 - 64*
x^5 - 32*x^6 + x^7 + (160000*x + 96000*x^2 + 19200*x^3 + 880*x^4 - 80*x^5)*Log[x] + (60000*x + 24000*x^2 + 240
0*x^3 - 50*x^4)*Log[x]^2 + (10000*x + 2000*x^2)*Log[x]^3 + 625*x*Log[x]^4)/(160000 + 128000*x + 38400*x^2 + 51
20*x^3 + 256*x^4 + (160000 + 96000*x + 19200*x^2 + 1280*x^3)*Log[x] + (60000 + 24000*x + 2400*x^2)*Log[x]^2 +
(10000 + 2000*x)*Log[x]^3 + 625*Log[x]^4)]),x]

[Out]

-4800*Defer[Int][1/((-8000 - 4800*x - 960*x^2 - 44*x^3 + 4*x^4 - 6000*Log[x] - 2400*x*Log[x] - 240*x^2*Log[x]
+ 5*x^3*Log[x] - 1500*Log[x]^2 - 300*x*Log[x]^2 - 125*Log[x]^3)*Log[(x*(400 + 160*x + 16*x^2 - x^3 + 40*(5 + x
)*Log[x] + 25*Log[x]^2)^2)/(4*(5 + x) + 5*Log[x])^4]), x] - 8000*Defer[Int][1/(x*(-8000 - 4800*x - 960*x^2 - 4
4*x^3 + 4*x^4 - 6000*Log[x] - 2400*x*Log[x] - 240*x^2*Log[x] + 5*x^3*Log[x] - 1500*Log[x]^2 - 300*x*Log[x]^2 -
125*Log[x]^3)*Log[(x*(400 + 160*x + 16*x^2 - x^3 + 40*(5 + x)*Log[x] + 25*Log[x]^2)^2)/(4*(5 + x) + 5*Log[x])
^4]), x] - 960*Defer[Int][x/((-8000 - 4800*x - 960*x^2 - 44*x^3 + 4*x^4 - 6000*Log[x] - 2400*x*Log[x] - 240*x^
2*Log[x] + 5*x^3*Log[x] - 1500*Log[x]^2 - 300*x*Log[x]^2 - 125*Log[x]^3)*Log[(x*(400 + 160*x + 16*x^2 - x^3 +
40*(5 + x)*Log[x] + 25*Log[x]^2)^2)/(4*(5 + x) + 5*Log[x])^4]), x] + 56*Defer[Int][x^2/((-8000 - 4800*x - 960*
x^2 - 44*x^3 + 4*x^4 - 6000*Log[x] - 2400*x*Log[x] - 240*x^2*Log[x] + 5*x^3*Log[x] - 1500*Log[x]^2 - 300*x*Log
[x]^2 - 125*Log[x]^3)*Log[(x*(400 + 160*x + 16*x^2 - x^3 + 40*(5 + x)*Log[x] + 25*Log[x]^2)^2)/(4*(5 + x) + 5*
Log[x])^4]), x] + 12*Defer[Int][x^3/((-8000 - 4800*x - 960*x^2 - 44*x^3 + 4*x^4 - 6000*Log[x] - 2400*x*Log[x]
- 240*x^2*Log[x] + 5*x^3*Log[x] - 1500*Log[x]^2 - 300*x*Log[x]^2 - 125*Log[x]^3)*Log[(x*(400 + 160*x + 16*x^2
- x^3 + 40*(5 + x)*Log[x] + 25*Log[x]^2)^2)/(4*(5 + x) + 5*Log[x])^4]), x] - 6000*Defer[Int][Log[x]/(x*(-8000
- 4800*x - 960*x^2 - 44*x^3 + 4*x^4 - 6000*Log[x] - 2400*x*Log[x] - 240*x^2*Log[x] + 5*x^3*Log[x] - 1500*Log[x
]^2 - 300*x*Log[x]^2 - 125*Log[x]^3)*Log[(x*(400 + 160*x + 16*x^2 - x^3 + 40*(5 + x)*Log[x] + 25*Log[x]^2)^2)/
(4*(5 + x) + 5*Log[x])^4]), x] - 240*Defer[Int][(x*Log[x])/((-8000 - 4800*x - 960*x^2 - 44*x^3 + 4*x^4 - 6000*
Log[x] - 2400*x*Log[x] - 240*x^2*Log[x] + 5*x^3*Log[x] - 1500*Log[x]^2 - 300*x*Log[x]^2 - 125*Log[x]^3)*Log[(x
*(400 + 160*x + 16*x^2 - x^3 + 40*(5 + x)*Log[x] + 25*Log[x]^2)^2)/(4*(5 + x) + 5*Log[x])^4]), x] + 35*Defer[I
nt][(x^2*Log[x])/((-8000 - 4800*x - 960*x^2 - 44*x^3 + 4*x^4 - 6000*Log[x] - 2400*x*Log[x] - 240*x^2*Log[x] +
5*x^3*Log[x] - 1500*Log[x]^2 - 300*x*Log[x]^2 - 125*Log[x]^3)*Log[(x*(400 + 160*x + 16*x^2 - x^3 + 40*(5 + x)*
Log[x] + 25*Log[x]^2)^2)/(4*(5 + x) + 5*Log[x])^4]), x] - 1500*Defer[Int][Log[x]^2/(x*(-8000 - 4800*x - 960*x^
2 - 44*x^3 + 4*x^4 - 6000*Log[x] - 2400*x*Log[x] - 240*x^2*Log[x] + 5*x^3*Log[x] - 1500*Log[x]^2 - 300*x*Log[x
]^2 - 125*Log[x]^3)*Log[(x*(400 + 160*x + 16*x^2 - x^3 + 40*(5 + x)*Log[x] + 25*Log[x]^2)^2)/(4*(5 + x) + 5*Lo
g[x])^4]), x] - 125*Defer[Int][Log[x]^3/(x*(-8000 - 4800*x - 960*x^2 - 44*x^3 + 4*x^4 - 6000*Log[x] - 2400*x*L
og[x] - 240*x^2*Log[x] + 5*x^3*Log[x] - 1500*Log[x]^2 - 300*x*Log[x]^2 - 125*Log[x]^3)*Log[(x*(400 + 160*x + 1
6*x^2 - x^3 + 40*(5 + x)*Log[x] + 25*Log[x]^2)^2)/(4*(5 + x) + 5*Log[x])^4]), x] + 2400*Defer[Int][Log[x]/((80
00 + 4800*x + 960*x^2 + 44*x^3 - 4*x^4 + 6000*Log[x] + 2400*x*Log[x] + 240*x^2*Log[x] - 5*x^3*Log[x] + 1500*Lo
g[x]^2 + 300*x*Log[x]^2 + 125*Log[x]^3)*Log[(x*(400 + 160*x + 16*x^2 - x^3 + 40*(5 + x)*Log[x] + 25*Log[x]^2)^
2)/(4*(5 + x) + 5*Log[x])^4]), x] + 300*Defer[Int][Log[x]^2/((8000 + 4800*x + 960*x^2 + 44*x^3 - 4*x^4 + 6000*
Log[x] + 2400*x*Log[x] + 240*x^2*Log[x] - 5*x^3*Log[x] + 1500*Log[x]^2 + 300*x*Log[x]^2 + 125*Log[x]^3)*Log[(x
*(400 + 160*x + 16*x^2 - x^3 + 40*(5 + x)*Log[x] + 25*Log[x]^2)^2)/(4*(5 + x) + 5*Log[x])^4]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-8000-4800 x-960 x^2+56 x^3+12 x^4+5 \left (-1200-480 x-48 x^2+7 x^3\right ) \log (x)-300 (5+x) \log ^2(x)-125 \log ^3(x)}{x \left (4 \left (-2000-1200 x-240 x^2-11 x^3+x^4\right )+5 \left (-1200-480 x-48 x^2+x^3\right ) \log (x)-300 (5+x) \log ^2(x)-125 \log ^3(x)\right ) \log \left (\frac {x \left (400+160 x+16 x^2-x^3+40 (5+x) \log (x)+25 \log ^2(x)\right )^2}{(4 (5+x)+5 \log (x))^4}\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.13, size = 46, normalized size = 1.64 \begin {gather*} \log \left (\log \left (\frac {x \left (400+160 x+16 x^2-x^3+40 (5+x) \log (x)+25 \log ^2(x)\right )^2}{(4 (5+x)+5 \log (x))^4}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(8000 + 4800*x + 960*x^2 - 56*x^3 - 12*x^4 + (6000 + 2400*x + 240*x^2 - 35*x^3)*Log[x] + (1500 + 300
*x)*Log[x]^2 + 125*Log[x]^3)/((8000*x + 4800*x^2 + 960*x^3 + 44*x^4 - 4*x^5 + (6000*x + 2400*x^2 + 240*x^3 - 5
*x^4)*Log[x] + (1500*x + 300*x^2)*Log[x]^2 + 125*x*Log[x]^3)*Log[(160000*x + 128000*x^2 + 38400*x^3 + 4320*x^4
- 64*x^5 - 32*x^6 + x^7 + (160000*x + 96000*x^2 + 19200*x^3 + 880*x^4 - 80*x^5)*Log[x] + (60000*x + 24000*x^2
+ 2400*x^3 - 50*x^4)*Log[x]^2 + (10000*x + 2000*x^2)*Log[x]^3 + 625*x*Log[x]^4)/(160000 + 128000*x + 38400*x^
2 + 5120*x^3 + 256*x^4 + (160000 + 96000*x + 19200*x^2 + 1280*x^3)*Log[x] + (60000 + 24000*x + 2400*x^2)*Log[x
]^2 + (10000 + 2000*x)*Log[x]^3 + 625*Log[x]^4)]),x]

[Out]

Log[Log[(x*(400 + 160*x + 16*x^2 - x^3 + 40*(5 + x)*Log[x] + 25*Log[x]^2)^2)/(4*(5 + x) + 5*Log[x])^4]]

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fricas [B]  time = 1.08, size = 172, normalized size = 6.14 \begin {gather*} \log \left (\log \left (\frac {x^{7} - 32 \, x^{6} - 64 \, x^{5} + 625 \, x \log \relax (x)^{4} + 4320 \, x^{4} + 2000 \, {\left (x^{2} + 5 \, x\right )} \log \relax (x)^{3} + 38400 \, x^{3} - 50 \, {\left (x^{4} - 48 \, x^{3} - 480 \, x^{2} - 1200 \, x\right )} \log \relax (x)^{2} + 128000 \, x^{2} - 80 \, {\left (x^{5} - 11 \, x^{4} - 240 \, x^{3} - 1200 \, x^{2} - 2000 \, x\right )} \log \relax (x) + 160000 \, x}{256 \, x^{4} + 2000 \, {\left (x + 5\right )} \log \relax (x)^{3} + 625 \, \log \relax (x)^{4} + 5120 \, x^{3} + 2400 \, {\left (x^{2} + 10 \, x + 25\right )} \log \relax (x)^{2} + 38400 \, x^{2} + 1280 \, {\left (x^{3} + 15 \, x^{2} + 75 \, x + 125\right )} \log \relax (x) + 128000 \, x + 160000}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((125*log(x)^3+(300*x+1500)*log(x)^2+(-35*x^3+240*x^2+2400*x+6000)*log(x)-12*x^4-56*x^3+960*x^2+4800*
x+8000)/(125*x*log(x)^3+(300*x^2+1500*x)*log(x)^2+(-5*x^4+240*x^3+2400*x^2+6000*x)*log(x)-4*x^5+44*x^4+960*x^3
+4800*x^2+8000*x)/log((625*x*log(x)^4+(2000*x^2+10000*x)*log(x)^3+(-50*x^4+2400*x^3+24000*x^2+60000*x)*log(x)^
2+(-80*x^5+880*x^4+19200*x^3+96000*x^2+160000*x)*log(x)+x^7-32*x^6-64*x^5+4320*x^4+38400*x^3+128000*x^2+160000
*x)/(625*log(x)^4+(2000*x+10000)*log(x)^3+(2400*x^2+24000*x+60000)*log(x)^2+(1280*x^3+19200*x^2+96000*x+160000
)*log(x)+256*x^4+5120*x^3+38400*x^2+128000*x+160000)),x, algorithm="fricas")

[Out]

log(log((x^7 - 32*x^6 - 64*x^5 + 625*x*log(x)^4 + 4320*x^4 + 2000*(x^2 + 5*x)*log(x)^3 + 38400*x^3 - 50*(x^4 -
48*x^3 - 480*x^2 - 1200*x)*log(x)^2 + 128000*x^2 - 80*(x^5 - 11*x^4 - 240*x^3 - 1200*x^2 - 2000*x)*log(x) + 1
60000*x)/(256*x^4 + 2000*(x + 5)*log(x)^3 + 625*log(x)^4 + 5120*x^3 + 2400*(x^2 + 10*x + 25)*log(x)^2 + 38400*
x^2 + 1280*(x^3 + 15*x^2 + 75*x + 125)*log(x) + 128000*x + 160000)))

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giac [B]  time = 13.70, size = 202, normalized size = 7.21 \begin {gather*} \log \left (-\log \left (x^{6} - 32 \, x^{5} - 80 \, x^{4} \log \relax (x) - 50 \, x^{3} \log \relax (x)^{2} - 64 \, x^{4} + 880 \, x^{3} \log \relax (x) + 2400 \, x^{2} \log \relax (x)^{2} + 2000 \, x \log \relax (x)^{3} + 625 \, \log \relax (x)^{4} + 4320 \, x^{3} + 19200 \, x^{2} \log \relax (x) + 24000 \, x \log \relax (x)^{2} + 10000 \, \log \relax (x)^{3} + 38400 \, x^{2} + 96000 \, x \log \relax (x) + 60000 \, \log \relax (x)^{2} + 128000 \, x + 160000 \, \log \relax (x) + 160000\right ) + \log \left (256 \, x^{4} + 1280 \, x^{3} \log \relax (x) + 2400 \, x^{2} \log \relax (x)^{2} + 2000 \, x \log \relax (x)^{3} + 625 \, \log \relax (x)^{4} + 5120 \, x^{3} + 19200 \, x^{2} \log \relax (x) + 24000 \, x \log \relax (x)^{2} + 10000 \, \log \relax (x)^{3} + 38400 \, x^{2} + 96000 \, x \log \relax (x) + 60000 \, \log \relax (x)^{2} + 128000 \, x + 160000 \, \log \relax (x) + 160000\right ) - \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((125*log(x)^3+(300*x+1500)*log(x)^2+(-35*x^3+240*x^2+2400*x+6000)*log(x)-12*x^4-56*x^3+960*x^2+4800*
x+8000)/(125*x*log(x)^3+(300*x^2+1500*x)*log(x)^2+(-5*x^4+240*x^3+2400*x^2+6000*x)*log(x)-4*x^5+44*x^4+960*x^3
+4800*x^2+8000*x)/log((625*x*log(x)^4+(2000*x^2+10000*x)*log(x)^3+(-50*x^4+2400*x^3+24000*x^2+60000*x)*log(x)^
2+(-80*x^5+880*x^4+19200*x^3+96000*x^2+160000*x)*log(x)+x^7-32*x^6-64*x^5+4320*x^4+38400*x^3+128000*x^2+160000
*x)/(625*log(x)^4+(2000*x+10000)*log(x)^3+(2400*x^2+24000*x+60000)*log(x)^2+(1280*x^3+19200*x^2+96000*x+160000
)*log(x)+256*x^4+5120*x^3+38400*x^2+128000*x+160000)),x, algorithm="giac")

[Out]

log(-log(x^6 - 32*x^5 - 80*x^4*log(x) - 50*x^3*log(x)^2 - 64*x^4 + 880*x^3*log(x) + 2400*x^2*log(x)^2 + 2000*x
*log(x)^3 + 625*log(x)^4 + 4320*x^3 + 19200*x^2*log(x) + 24000*x*log(x)^2 + 10000*log(x)^3 + 38400*x^2 + 96000
*x*log(x) + 60000*log(x)^2 + 128000*x + 160000*log(x) + 160000) + log(256*x^4 + 1280*x^3*log(x) + 2400*x^2*log
(x)^2 + 2000*x*log(x)^3 + 625*log(x)^4 + 5120*x^3 + 19200*x^2*log(x) + 24000*x*log(x)^2 + 10000*log(x)^3 + 384
00*x^2 + 96000*x*log(x) + 60000*log(x)^2 + 128000*x + 160000*log(x) + 160000) - log(x))

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maple [C]  time = 0.59, size = 1165, normalized size = 41.61

method	result	size
risch	\(\ln \left (\ln \left (x^{3}-16 x^{2}+\left (-40 \ln \relax (x )-160\right ) x -25 \ln \relax (x )^{2}-200 \ln \relax (x )-400\right )-\frac {i \left (2 i \ln \relax (x )+\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right ) \mathrm {csgn}\left (\frac {i x \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right )+\pi \,\mathrm {csgn}\left (\frac {i}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right ) \mathrm {csgn}\left (i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}\right ) \mathrm {csgn}\left (\frac {i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right )-\pi \,\mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )\right ) \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{3}\right ) \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}\right )-\pi \,\mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )\right ) \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{2}\right ) \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{3}\right )+\pi \mathrm {csgn}\left (i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )\right )^{2} \mathrm {csgn}\left (i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}\right )+\pi \,\mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )\right ) \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}\right )^{2}+\pi \,\mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{3}\right ) \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}\right )^{2}-\pi \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )\right )^{2} \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{2}\right )+2 \pi \,\mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )\right ) \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{2}\right )^{2}+\pi \,\mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )\right ) \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{3}\right )^{2}+\pi \,\mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{2}\right ) \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{3}\right )^{2}+2 \pi \,\mathrm {csgn}\left (i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )\right ) \mathrm {csgn}\left (i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}\right )^{2}-\pi \,\mathrm {csgn}\left (\frac {i}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right ) \mathrm {csgn}\left (\frac {i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}\right ) \mathrm {csgn}\left (\frac {i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right )^{2}-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (\frac {i x \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right )^{2}-\pi \,\mathrm {csgn}\left (\frac {i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right ) \mathrm {csgn}\left (\frac {i x \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right )^{2}-16 i \ln \relax (2)-8 i \ln \left (x +\frac {5 \ln \relax (x )}{4}+5\right )+\pi \mathrm {csgn}\left (i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}\right )^{3}+\pi \mathrm {csgn}\left (\frac {i x \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right )^{3}+\pi \mathrm {csgn}\left (\frac {i \left (-x^{3}+16 x^{2}-\left (-40 \ln \relax (x )-160\right ) x +25 \ln \relax (x )^{2}+200 \ln \relax (x )+400\right )^{2}}{\left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}}\right )^{3}-\pi \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{3}\right )^{3}-\pi \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{4}\right )^{3}-\pi \mathrm {csgn}\left (i \left (x +\frac {5 \ln \relax (x )}{4}+5\right )^{2}\right )^{3}\right )}{4}\right )\)	\(1165\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((125*ln(x)^3+(300*x+1500)*ln(x)^2+(-35*x^3+240*x^2+2400*x+6000)*ln(x)-12*x^4-56*x^3+960*x^2+4800*x+8000)/(
125*x*ln(x)^3+(300*x^2+1500*x)*ln(x)^2+(-5*x^4+240*x^3+2400*x^2+6000*x)*ln(x)-4*x^5+44*x^4+960*x^3+4800*x^2+80
00*x)/ln((625*x*ln(x)^4+(2000*x^2+10000*x)*ln(x)^3+(-50*x^4+2400*x^3+24000*x^2+60000*x)*ln(x)^2+(-80*x^5+880*x
^4+19200*x^3+96000*x^2+160000*x)*ln(x)+x^7-32*x^6-64*x^5+4320*x^4+38400*x^3+128000*x^2+160000*x)/(625*ln(x)^4+
(2000*x+10000)*ln(x)^3+(2400*x^2+24000*x+60000)*ln(x)^2+(1280*x^3+19200*x^2+96000*x+160000)*ln(x)+256*x^4+5120
*x^3+38400*x^2+128000*x+160000)),x,method=_RETURNVERBOSE)

[Out]

ln(ln(x^3-16*x^2+(-40*ln(x)-160)*x-25*ln(x)^2-200*ln(x)-400)-1/4*I*(Pi*csgn(I*x)*csgn(I/(x+5/4*ln(x)+5)^4*(-x^
3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400)^2)*csgn(I*x*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200
*ln(x)+400)^2/(x+5/4*ln(x)+5)^4)+Pi*csgn(I/(x+5/4*ln(x)+5)^4)*csgn(I*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2
+200*ln(x)+400)^2)*csgn(I/(x+5/4*ln(x)+5)^4*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400)^2)-Pi*csg
n(I*(x+5/4*ln(x)+5))*csgn(I*(x+5/4*ln(x)+5)^3)*csgn(I*(x+5/4*ln(x)+5)^4)-Pi*csgn(I*(x+5/4*ln(x)+5))*csgn(I*(x+
5/4*ln(x)+5)^2)*csgn(I*(x+5/4*ln(x)+5)^3)+Pi*csgn(I*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400))^
2*csgn(I*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400)^2)-16*I*ln(2)-8*I*ln(x+5/4*ln(x)+5)+2*I*ln(x
)+Pi*csgn(I*(x+5/4*ln(x)+5))*csgn(I*(x+5/4*ln(x)+5)^4)^2+Pi*csgn(I*(x+5/4*ln(x)+5)^3)*csgn(I*(x+5/4*ln(x)+5)^4
)^2-Pi*csgn(I*(x+5/4*ln(x)+5))^2*csgn(I*(x+5/4*ln(x)+5)^2)+2*Pi*csgn(I*(x+5/4*ln(x)+5))*csgn(I*(x+5/4*ln(x)+5)
^2)^2+Pi*csgn(I*(x+5/4*ln(x)+5))*csgn(I*(x+5/4*ln(x)+5)^3)^2+Pi*csgn(I*(x+5/4*ln(x)+5)^2)*csgn(I*(x+5/4*ln(x)+
5)^3)^2+2*Pi*csgn(I*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400))*csgn(I*(-x^3+16*x^2-(-40*ln(x)-1
60)*x+25*ln(x)^2+200*ln(x)+400)^2)^2-Pi*csgn(I/(x+5/4*ln(x)+5)^4)*csgn(I/(x+5/4*ln(x)+5)^4*(-x^3+16*x^2-(-40*l
n(x)-160)*x+25*ln(x)^2+200*ln(x)+400)^2)^2-Pi*csgn(I*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400)^
2)*csgn(I/(x+5/4*ln(x)+5)^4*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400)^2)^2-Pi*csgn(I*x)*csgn(I*
x*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400)^2/(x+5/4*ln(x)+5)^4)^2-Pi*csgn(I/(x+5/4*ln(x)+5)^4*
(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400)^2)*csgn(I*x*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2
+200*ln(x)+400)^2/(x+5/4*ln(x)+5)^4)^2+Pi*csgn(I*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400)^2)^3
+Pi*csgn(I*x*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400)^2/(x+5/4*ln(x)+5)^4)^3+Pi*csgn(I/(x+5/4*
ln(x)+5)^4*(-x^3+16*x^2-(-40*ln(x)-160)*x+25*ln(x)^2+200*ln(x)+400)^2)^3-Pi*csgn(I*(x+5/4*ln(x)+5)^3)^3-Pi*csg
n(I*(x+5/4*ln(x)+5)^4)^3-Pi*csgn(I*(x+5/4*ln(x)+5)^2)^3))

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maxima [A]  time = 13.52, size = 47, normalized size = 1.68 \begin {gather*} \log \left (\log \left (-x^{3} + 16 \, x^{2} + 40 \, {\left (x + 5\right )} \log \relax (x) + 25 \, \log \relax (x)^{2} + 160 \, x + 400\right ) - 2 \, \log \left (4 \, x + 5 \, \log \relax (x) + 20\right ) + \frac {1}{2} \, \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((125*log(x)^3+(300*x+1500)*log(x)^2+(-35*x^3+240*x^2+2400*x+6000)*log(x)-12*x^4-56*x^3+960*x^2+4800*
x+8000)/(125*x*log(x)^3+(300*x^2+1500*x)*log(x)^2+(-5*x^4+240*x^3+2400*x^2+6000*x)*log(x)-4*x^5+44*x^4+960*x^3
+4800*x^2+8000*x)/log((625*x*log(x)^4+(2000*x^2+10000*x)*log(x)^3+(-50*x^4+2400*x^3+24000*x^2+60000*x)*log(x)^
2+(-80*x^5+880*x^4+19200*x^3+96000*x^2+160000*x)*log(x)+x^7-32*x^6-64*x^5+4320*x^4+38400*x^3+128000*x^2+160000
*x)/(625*log(x)^4+(2000*x+10000)*log(x)^3+(2400*x^2+24000*x+60000)*log(x)^2+(1280*x^3+19200*x^2+96000*x+160000
)*log(x)+256*x^4+5120*x^3+38400*x^2+128000*x+160000)),x, algorithm="maxima")

[Out]

log(log(-x^3 + 16*x^2 + 40*(x + 5)*log(x) + 25*log(x)^2 + 160*x + 400) - 2*log(4*x + 5*log(x) + 20) + 1/2*log(
x))

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mupad [B]  time = 10.03, size = 178, normalized size = 6.36 \begin {gather*} \ln \left (\ln \left (\frac {160000\,x+{\ln \relax (x)}^3\,\left (2000\,x^2+10000\,x\right )+625\,x\,{\ln \relax (x)}^4+\ln \relax (x)\,\left (-80\,x^5+880\,x^4+19200\,x^3+96000\,x^2+160000\,x\right )+{\ln \relax (x)}^2\,\left (-50\,x^4+2400\,x^3+24000\,x^2+60000\,x\right )+128000\,x^2+38400\,x^3+4320\,x^4-64\,x^5-32\,x^6+x^7}{128000\,x+{\ln \relax (x)}^2\,\left (2400\,x^2+24000\,x+60000\right )+625\,{\ln \relax (x)}^4+38400\,x^2+5120\,x^3+256\,x^4+{\ln \relax (x)}^3\,\left (2000\,x+10000\right )+\ln \relax (x)\,\left (1280\,x^3+19200\,x^2+96000\,x+160000\right )+160000}\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4800*x + 125*log(x)^3 + 960*x^2 - 56*x^3 - 12*x^4 + log(x)^2*(300*x + 1500) + log(x)*(2400*x + 240*x^2 -
35*x^3 + 6000) + 8000)/(log((160000*x + log(x)^3*(10000*x + 2000*x^2) + 625*x*log(x)^4 + log(x)*(160000*x + 96
000*x^2 + 19200*x^3 + 880*x^4 - 80*x^5) + log(x)^2*(60000*x + 24000*x^2 + 2400*x^3 - 50*x^4) + 128000*x^2 + 38
400*x^3 + 4320*x^4 - 64*x^5 - 32*x^6 + x^7)/(128000*x + log(x)^2*(24000*x + 2400*x^2 + 60000) + 625*log(x)^4 +
38400*x^2 + 5120*x^3 + 256*x^4 + log(x)^3*(2000*x + 10000) + log(x)*(96000*x + 19200*x^2 + 1280*x^3 + 160000)
+ 160000))*(8000*x + log(x)^2*(1500*x + 300*x^2) + 125*x*log(x)^3 + log(x)*(6000*x + 2400*x^2 + 240*x^3 - 5*x
^4) + 4800*x^2 + 960*x^3 + 44*x^4 - 4*x^5)),x)

[Out]

log(log((160000*x + log(x)^3*(10000*x + 2000*x^2) + 625*x*log(x)^4 + log(x)*(160000*x + 96000*x^2 + 19200*x^3
+ 880*x^4 - 80*x^5) + log(x)^2*(60000*x + 24000*x^2 + 2400*x^3 - 50*x^4) + 128000*x^2 + 38400*x^3 + 4320*x^4 -
64*x^5 - 32*x^6 + x^7)/(128000*x + log(x)^2*(24000*x + 2400*x^2 + 60000) + 625*log(x)^4 + 38400*x^2 + 5120*x^
3 + 256*x^4 + log(x)^3*(2000*x + 10000) + log(x)*(96000*x + 19200*x^2 + 1280*x^3 + 160000) + 160000)))

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sympy [B]  time = 6.54, size = 178, normalized size = 6.36 \begin {gather*} \log {\left (\log {\left (\frac {x^{7} - 32 x^{6} - 64 x^{5} + 4320 x^{4} + 38400 x^{3} + 128000 x^{2} + 625 x \log {\relax (x )}^{4} + 160000 x + \left (2000 x^{2} + 10000 x\right ) \log {\relax (x )}^{3} + \left (- 50 x^{4} + 2400 x^{3} + 24000 x^{2} + 60000 x\right ) \log {\relax (x )}^{2} + \left (- 80 x^{5} + 880 x^{4} + 19200 x^{3} + 96000 x^{2} + 160000 x\right ) \log {\relax (x )}}{256 x^{4} + 5120 x^{3} + 38400 x^{2} + 128000 x + \left (2000 x + 10000\right ) \log {\relax (x )}^{3} + \left (2400 x^{2} + 24000 x + 60000\right ) \log {\relax (x )}^{2} + \left (1280 x^{3} + 19200 x^{2} + 96000 x + 160000\right ) \log {\relax (x )} + 625 \log {\relax (x )}^{4} + 160000} \right )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((125*ln(x)**3+(300*x+1500)*ln(x)**2+(-35*x**3+240*x**2+2400*x+6000)*ln(x)-12*x**4-56*x**3+960*x**2+4
800*x+8000)/(125*x*ln(x)**3+(300*x**2+1500*x)*ln(x)**2+(-5*x**4+240*x**3+2400*x**2+6000*x)*ln(x)-4*x**5+44*x**
4+960*x**3+4800*x**2+8000*x)/ln((625*x*ln(x)**4+(2000*x**2+10000*x)*ln(x)**3+(-50*x**4+2400*x**3+24000*x**2+60
000*x)*ln(x)**2+(-80*x**5+880*x**4+19200*x**3+96000*x**2+160000*x)*ln(x)+x**7-32*x**6-64*x**5+4320*x**4+38400*
x**3+128000*x**2+160000*x)/(625*ln(x)**4+(2000*x+10000)*ln(x)**3+(2400*x**2+24000*x+60000)*ln(x)**2+(1280*x**3
+19200*x**2+96000*x+160000)*ln(x)+256*x**4+5120*x**3+38400*x**2+128000*x+160000)),x)

[Out]

log(log((x**7 - 32*x**6 - 64*x**5 + 4320*x**4 + 38400*x**3 + 128000*x**2 + 625*x*log(x)**4 + 160000*x + (2000*
x**2 + 10000*x)*log(x)**3 + (-50*x**4 + 2400*x**3 + 24000*x**2 + 60000*x)*log(x)**2 + (-80*x**5 + 880*x**4 + 1
9200*x**3 + 96000*x**2 + 160000*x)*log(x))/(256*x**4 + 5120*x**3 + 38400*x**2 + 128000*x + (2000*x + 10000)*lo
g(x)**3 + (2400*x**2 + 24000*x + 60000)*log(x)**2 + (1280*x**3 + 19200*x**2 + 96000*x + 160000)*log(x) + 625*l
og(x)**4 + 160000)))

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